Algebra 2 & Algebra 2 Honors Summer Assignment · Algebra 2 & Algebra 2 Honors Summer Assignment...
Transcript of Algebra 2 & Algebra 2 Honors Summer Assignment · Algebra 2 & Algebra 2 Honors Summer Assignment...
Algebra 2 & Algebra 2 Honors Summer Assignment
Congratulations on signing up to take Algebra 2!
The purpose of this math assignment is to set the stage for instruction for the 2019-2020 school year. This assignment is a review of previously taught Algebra 1 concepts. These concepts are required to be successful in the upcoming year. If you do not know these concepts or have forgotten them, you need to try to re-learn them over the summer. The site www.purplemath.com provides videos explaining how to do many algebra topics. We suggest you download and print the packet early in the summer so you can start the assignment and pace your work throughout the summer. The completed packet is due on the first day of school and will be your first project grade. Make sure you show your work where appropriate and use notebook paper when there is not enough room for your process in the worksheets. You will not be given credit if you don't show work on problems that require it. It is expected that you have a good understanding of this material coming into Algebra 2, as teachers will not be doing an extensive review of previously learned material.
Have a great summer and we look forward to seeing you in the fall!
UHS Algebra 2 Team
Name _______________________________________ Date ___________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
17 Holt McDougal Algebra 1
Foundations of Algebra
1. Samir swam m fewer laps than his friend
Kristen, who swam 8 laps. Write an
expression for the number of laps Samir
swam.
________________________________________
2. Write two verbal expressions for
k
10.
________________________________________
________________________________________
3. Evaluate p + q for p = 1.4 and q = 0.1.
________________________________________
Add or subtract.
4. −17 − (−17)
________________________________________
5. 5.1 − 7.5
________________________________________
6.
3
5 −
2
15
________________________________________
Multiply or divide.
7. 14
−1
2
________________________________________
8. −20 ÷ 1
22
−
________________________________________
9. 12.5 ÷ (−4)
________________________________________
10. John bikes 25 mi/h for a 3.5 hour trip.
How many miles does he travel?
________________________________________
Evaluate each expression.
11. (−2)6
________________________________________
12. 2
7
13
−
________________________________________
13. Find − 1.44 .
________________________________________
Classify each real number. Write all classifications that apply.
14. −
4
3
________________________________________
________________________________________
15. 0
________________________________________
________________________________________
16. A coffee table is shaped like a square
and has an area of 22 square feet. Find
the length of the side of the table to the
nearest tenth of a foot.
________________________________________
17. U is the set of positive integers less than
18. G is the set of positive factors of 12.
What is the complement of set G in
universe U.
________________________________________
SECTION
1
Name _______________________________________ Date ___________________ Class __________________
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18 Holt McDougal Algebra 1
Foundations of Algebra continued
18. F is the set of positive factors of 24
and G is the set of perfect squares
less than 12. Is the statement F ⊂ G
true or false?
________________________________________
19. Simplify 2|42 − 21| ÷ 34 − 9 .
________________________________________
20. Evaluate x + 22 − 4 for x = 5.
________________________________________
21. Translate “the square root of the quotient
of −s and −15” into an algebraic
expression.
________________________________________
22. The expression πr2h can be used to find
the volume of a cylinder, where r is the
radius and h is the height of the cylinder.
If a cylinder has a radius of 2 inches and
a height of 7 inches, find its volume. (Use
3.14 for π and give your final answer to
the nearest tenth.)
________________________________________
Simplify each expression.
23.
1
4 • 30 •
2
3
________________________________________
24. 1.5x − 8(3 − 0.2x)
________________________________________
25.
1
2(−12x + y) − 5y
________________________________________
Use this coordinate plane for questions 26 and 27.
26. What are the coordinates of point A?
________________________________________
27. In which quadrant does point B lie?
________________________________________
28. Generate ordered pairs for the function
y = −|x| using x = −2, −1, 0, 1,
and 2.
Graph the ordered pairs and describe
the pattern.
________________________________________
________________________________________
SECTION
1
Name _______________________________________ Date __________________ Class __________________
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37 Holt McDougal Algebra 1
Equations
Solve each equation.
1. x − 39 = −105
________________________________________
2. 11.5 = a + 4.5
________________________________________
3. Write an equation to represent the
relationship “a number decreased by
negative 2 is equal to 21.” Then solve
the equation.
________________________________________
________________________________________
Solve each equation.
4.
m
4 = −7
________________________________________
5. −4.8t = 9.6
________________________________________
6. Write an equation to represent the
relationship “the product of a number
and −2.5 is 60.” Then solve the
equation.
________________________________________
________________________________________
Solve each equation.
7. 9(z − 1) + 2z + 16 = 62
________________________________________
8.
7
5 =
d
10 −
3d
2
________________________________________
9. A printing company charges $42 plus
$0.05 per page. Another company just
charges $0.08 per page. How many
pages are in an order that costs the
same regardless of which company is
used?
________________________________________
Solve each equation.
10. 10a − 35 = −8a + 1
________________________________________
11. 5(x + 1) = 5(x + 5) − 15
________________________________________
12. Solve S =
n
2(a + b) for b.
________________________________________
13. Solve 0.30x + 6y = 300 for x.
________________________________________
14. A boat travels 66 miles in 2 hours. What
is its rate in feet per minute?
________________________________________
15. What is the solution to 3 x −12 + 7 = 7?
________________________________________
16. What is the solution to 2 x + 3 − 4 = −6?
________________________________________
SECTION
2
Name _______________________________________ Date __________________ Class __________________
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38 Holt McDougal Algebra 1
Equations continued
17. Solve
3
−s +1 =
6
s + 4.
________________________________________
18. The ratio of students to faculty members
in a high school is 23:5. If there are 80
faculty members, how many students
are there?
________________________________________
19. A triangle has an area of 40 square
centimeters. Its dimensions are
multiplied by a scale factor, forming a
new triangle with an area of 640 square
centimeters. What was the scale factor?
________________________________________
20. A tree casts a shadow 8.5 ft long at the
same time that a nearby 3-foot-tall pole
casts a shadow 3.75 feet long. Write and
solve a proportion to find the height of
the tree.
________________________________________
________________________________________
21. Find the value of x in the diagram.
∆ABC ~ ∆ADE.
________________________________________
22. Sixteen is 1.6% of what number?
________________________________________
23. What is 500% of 10.5?
________________________________________
24. A realtor earns a 3.25% commission
on the sale of each house. How much
did a house sell for if the realtor earned
$10,566.40?
________________________________________
25. Estimate the tip on a $31.77 check using
a tip rate of 15%.
________________________________________
26. Find the percent change from 0.5 to 3.
Tell whether it is a percent increase or
decrease.
________________________________________
________________________________________
27. Find the result when 130 is decreased
by 15%.
________________________________________
28. Antonio sold skis for $220. His
wholesale cost was $165. What was the
percent markup?
________________________________________
29. Ali bought a suitcase that originally
cost $145. After she used a coupon,
she spent $116 on the suitcase. What
percent discount did she receive?
________________________________________
SECTION
2
Name _______________________________________ Date ___________________ Class __________________
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57 Holt McDougal Algebra 1
Inequalities
1. Describe the solutions of (2 − 5)2 ≤ t
in words.
________________________________________
________________________________________
Graph each inequality.
2. b ≤ −4
1
2
3. w > − 36
4. Write the inequality shown by the graph.
________________________________________
5. It is not safe to walk on ice if it is less
than 4 inches thick. Define a variable
and write an inequality for thickness of
ice on which it is safe to walk. Graph the
solutions.
________________________________________
________________________________________
Solve each inequality and graph the solutions.
6. 21 + x ≤ 21
________________________________________
7. 1
2
3< −4 + y
________________________________________
8. f + 4.5 ≥ |−3.5|
________________________________________
9. During the track season, Larry tries to
drink at least 8 cups of water each day.
So far today, he drank a 24-ounce bottle
of water. Write and solve an inequality
to determine how many more ounces of
water Larry must drink to fulfill his daily
goal. (Hint: 1 c = 8 oz)
________________________________________
________________________________________
Solve each inequality.
10. 20 > −40x
________________________________________
11.
7d
9 ≥ −35
________________________________________
SECTION
3
Name _______________________________________ Date ___________________ Class __________________
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58 Holt McDougal Algebra 1
Inequalities continued
12. Over the summer, Silvio earned $380
by mowing lawns and $80 by tutoring.
He wants to take an adventure vacation
which costs $45 per night. What are the
possible numbers of nights Silvio can
sign up for if he spends only the money
he earned over the summer?
________________________________________
________________________________________
Solve each inequality.
13.
1
2 >
−1+ 5n
2
________________________________________
14. −30 ≥ −4a + 18 − 2(23 − a)
________________________________________
15. The average of Cindy’s three test scores
must be greater than 70 for her to pass
the class. She got a 76 on the last test.
She got the same score on her first and
second test. She passed the class. What
scores could she have gotten on the first
two tests?
________________________________________
Solve each inequality.
16. 2(−x + 7) < −3x + 8 + x
________________________________________
17.
7
8 <
15
16 −
x
6
________________________________________
18. Lori rented a booth at the craft fair for
$200 to sell baskets she made. The cost
of the materials for each basket was
$8. If she sells the baskets for $20, how
many does she have to sell to make a
profit?
________________________________________
Solve each compound inequality and graph the solutions.
19. 2 < −2n + 20 ≤ 4
________________________________________
20. 4a + 1 > −15 OR
a
−3 ≥ 2.5
________________________________________
21. Write the compound inequality shown by
the graph.
________________________________________
Solve each compound inequality.
22. +3 2x − 1.8 > −4
________________________________________
23. + 9x − 13 < −18
________________________________________
SECTION
3
Name _______________________________________ Date __________________ Class __________________
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77 Holt McDougal Algebra 1
Functions
1. A roller coaster leaves the boarding area
at a steady speed. It moves slowly as it
climbs and increases speed as it
descends before coming to a stop at the
end of the ride. Choose the graph that
best represents this situation.
________________________________________
2. A gizmo sells for $1.25. Sketch a graph to
show the total cost if a customer buys
0, 1, 2, 3, or 4 gizmos. Tell whether the
graph is continuous or discrete.
________________________________________
3. Express the relation {(−2, 3), (2, 3), (5, 3),
(−2, 4)} as a mapping diagram.
4. Give the range of the relation.
________________________________________
5. Give the domain of the relation.
x −2 −1 0 3.5 4.2
y 2 2.1 5.1 5.5 6.0
________________________________________
6. Tell whether the relation is a function.
Explain.
{(−4, 0), (−3, 0), (−2, 1), (1, −2), (−3, 4)}
________________________________________
________________________________________
________________________________________
7. Determine a relationship between the
x- and y-values. Write an equation.
x 0 1 2 3 4
y 1 2 5 10 17
________________________________________
SECTION
4
Name _______________________________________ Date __________________ Class __________________
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78 Holt McDougal Algebra 1
Functions continued
Write a rule in function notation for each situation.
8. The cost of membership is $21 plus
$5.50 each month.
________________________________________
9. Sales tax is 7% of the total price.
________________________________________
10. For f(x) =
1
4x + 10, find x such that
f(x) = 14.
________________________________________
11. Identify the independent and dependent
variables.
The essay instructions were to write three
facts about each person listed.
________________________________________
________________________________________
Graph each function.
12. y =
x2
2 − 3; D: {−4, −2, 0, 2}
13. f(x) = |3 − x| + 1
14. The table shows the percent of raw
materials exported over a four year
period. Draw a scatter plot and trend line.
Year ’98 ’99 ’00 ’01
Raw Materials 60% 52% 54% 48%
Based on the trend line, predict the
percent of raw materials exported in
2004.
________________________________________
15. Find the next three terms of the
arithmetic sequence
1
8,
1
4,
3
8,
1
2, …
________________________________________
16. What is the 37th term of the arithmetic
sequence 4.1, 3, 1.9, 0.8,…?
________________________________________
SECTION
4
Name _______________________________________ Date __________________ Class __________________
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97 Holt McDougal Algebra 1
Linear Functions
1. Do these ordered pairs satisfy a linear
function? Explain.
{(0, 1), (1, 2), (2, 4), (3, 8), (4, 16)}
________________________________________
2. An apartment in Valparaiso, Indiana,
rents for $600 per month with a $1000
deposit. The rental is month-to-month,
but you must stay at least one month.
The function f(x) = 600x + 1000 gives the
cost of renting for x months.
Graph this function.
Give its domain and range.
domain: ________________________________
range: _________________________________
3. A machine makes 640 fl oz of yogurt.
Each serving is 8 fl oz. The amount left
after x servings is described by the
function f(x) = 640 − 8x. What is the value
and meaning of each intercept?
x-intercept: _____________________________
________________________________________
y-intercept: _____________________________
________________________________________
4. This table shows the percent interest
on a new 30-year homeowner’s loan
for different months after August 16,
2004. During which time interval did the
percent interest increase at the greatest
rate. What was the rate of change for
that interval?
Months after
8/16/2004 0 6 9 11 12
Interest (%) 5.46 5.14 5.30 5.27 5.37
________________________________________
5. Find the slope of this line.
________________________________________
6. Find the value of y so that the points
(−5, 10) and (3, y) lie on a line with
slope −
3
8.
________________________________________
7. M is the midpoint of QR and M has
coordinates (−2, 6). Q has coordinates
(8, −10). What are the coordinates of R?
________________________________________
SECTION
5
Name _______________________________________ Date __________________ Class __________________
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98 Holt McDougal Algebra 1
Linear Functions continued
8. Find the distance between the points
A(−12, 2) and B(−7, −10).
________________________________________
9. The value of y varies directly with x, and
y = 5.4 when x = 9. Find y when x = −10.
________________________________________
10. Write an equation in slope-intercept form
that describes the line with a slope of 3
and containing the point (5, −1).
________________________________________
11. Write the equation x − 3y = 9 in slope-
intercept form. Then graph the line
described by the equation.
________________________________________
12. Write an equation in point-slope form that
describes the line through the points
(−2, 6) and (3, 1).
________________________________________
13. Graph y + 1 = −3(x − 2).
14. Find the intercepts of the line that
contains the points A(4, 2) and B(−2, 5).
________________________________________
15. Identify which lines are parallel.
I 3y = 2x
II y = −
2
3x + 7
III y + 7 = −
3
2(x − 8)
IV 3x + 2y = 7
________________________________________
16. Write an equation in slope-intercept form
for the line that passes through
(5, −4) and is perpendicular to the line
described by 2x − 10y = 0.
________________________________________
SECTION
5
Name _______________________________________ Date __________________ Class __________________
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117 Holt McDougal Algebra 1
Systems of Equations and Inequalities
1. Tell whether (−
1
2,1) is a solution of
2x − y = −2
y − 4x = 3
.
________________________________________
2. Solve
y − 2 =1
3x
3y = −2x − 3
by graphing.
________________________________________
3. Solve by substitution:
−2x − y = 3
y − 12 = x
.
________________________________________
4. Solve by elimination:
3y − 4x = 29
2y + 5x = 4
.
________________________________________
5. A chemist has a 2% acid solution and an
8% acid solution. He wants to mix the
solutions to get 300 mL of a 5.5% acid
solution. How many milliliters of each
solution does he need?
________________________________________
6. Solve by any method:
y + x = 3
1
2y = −
1
3x
.
________________________________________
7. Classify
5y − 4x = −5
10y + 2 = 4x
.
________________________________________
SECTION
6
Name _______________________________________ Date __________________ Class __________________
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118 Holt McDougal Algebra 1
Systems of Equations and Inequalities continued
8. How many solutions does
3y = −6x −3
2y + 2x = 1
have?
________________________________________
9. Solve
6y − 4x = 6
9y = 6x + 9
.
________________________________________
10. Tell whether (10, 7
1
2) is a solution of
y ≥ −
1
4x − 5.
________________________________________
11. Write the inequality represented by the
graph below.
________________________________________
12. Tell whether (5,
1
3) is a solution of
y ≤ x − 4
−x + 3y > −4
.
________________________________________
13. Graph
y − 3x < 5
3x − y ≥ 7
.
Give two ordered pairs that are solutions
and two ordered pairs that are not
solutions.
________________________________________
________________________________________
14. An artist has 600 inches of framing
material to form a rectangular frame. The
dimensions of the wall on which it will
hang limit the frame’s width to no more
than
200 inches. The artist wants the length to
be at least 2 times longer than the width.
Write a system to represent this situation.
________________________________________
SECTION
6
Name _______________________________________ Date __________________ Class __________________
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137 Holt McDougal Algebra 1
Exponents and Polynomials
1. Simplify −5−−−−3.
________________________________________
2. Evaluate 4x0y−3 for x = −3 and y = 2.
________________________________________
3. Simplify
12a−2
b0.
________________________________________
4. Write 0.0000000000000000001 as a
power of 10.
________________________________________
5. The mass of Pluto is 0.0021 times the
mass of the Earth. Write this number in
scientific notation.
________________________________________
6. Write 9.803 × 1016 in standard form.
________________________________________
Simplify.
7. y8 • y−2 • y3
________________________________________
8. (x4)−2
________________________________________
9. (a−3b4)3 • (a2)5
________________________________________
10. In 2000, the population of Geneseo,
New York, was about 7600 people. The
population of the entire state of New York
was about 2.5 × 103 times larger than the
population of Geneseo. What was the
population of New York in 2000? Write
your answer in scientific notation.
________________________________________
Simplify.
11.
(a4b5 )3
a2b9
________________________________________
12.
x5y 3
x8y
3
________________________________________
13.
a2
3
−13a3
b5
−4
________________________________________
SECTION
7
Name _______________________________________ Date __________________ Class __________________
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138 Holt McDougal Algebra 1
Exponents and Polynomials continued
14. Simplify the quotient
(8.5 × 1016) ÷ (3.4 × 10−4). Write the
answer in scientific notation.
________________________________________
Simplify.
15.
________________________________________
16. 644
3
________________________________________
17. Simplify (x
1
3 y )3 x4y 6 . All variables
represent nonnegative numbers.
________________________________________
18. What is the leading coefficient of the
polynomial 7x2 − x5 − 9x + 4?
________________________________________
19. Classify the polynomial x5 + 3x2 + x − 2
according to its degree and number of
terms.
________________________________________
20. Jamal throws a golf ball straight up from
a height of 5 feet and at a speed of
75 feet per second. The height of the
ball in feet is given by the polynomial
−16t
2 + 75t + 5, where t is the time in
seconds. How high is the ball after
4 seconds?
________________________________________
21. Add (2.3x3 − 5x2 − 0.4) + (7x2 + 1.3).
________________________________________
22. Subtract (7a4 − a3 + 2) − (9a3 − a2 − 6).
________________________________________
23. Multiply (5r)(−4r
6s2)(3r
5s4).
________________________________________
24. A trapezoid has height h. One base is
4 units shorter than the height. The other
base is 5 times longer than the height.
Write a polynomial for the area of the
trapezoid.
________________________________________
Multiply.
25. (4x − 5)(7x + 4)
________________________________________
26. (2b − 1)3
________________________________________
27. (5x + 3y)2
________________________________________
28. (4p2 + 6q)(4p2 − 6q)
________________________________________
SECTION
7
Name _______________________________________ Date ___________________ Class __________________
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167 Holt McDougal Algebra 1
Factoring Polynomials
1. Write the prime factorization of 1575.
________________________________________
Find the GCF.
2. 420 and 1365
________________________________________
3. 102x
3 and 170x
2y
________________________________________
4. Jenny is displaying her photographs
on a table at a sidewalk art show. She
has 45 photos of people, 18 photos
of landscapes, and 63 photos of pets.
Each row will have the same number
of photos, but people, landscapes, and
pets will not appear in the same row. If
she puts the greatest possible number of
photos in each row, how many rows will
there be?
________________________________________
Factor.
5. −8y
3 + 12y
2 − 6
________________________________________
6. 5n(3n − 4) − 2(4 − 3n)
________________________________________
7. Factor 21a3 + 14a2 − 9a − 6 by
grouping.
________________________________________
Factor each trinomial.
8. x
2 + 46x + 525
________________________________________
9. x
2 − 11x + 60
________________________________________
10. x
2 − 11x − 126
________________________________________
11. Find an integer value of b that makes
x
2 + bx − 81 factorable, and then factor
the trinomial.
b = ____________________________________
________________________________________
12. Factor 14x
2 − 57x + 45.
________________________________________
SECTION
8
Name _______________________________________ Date ___________________ Class __________________
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168 Holt McDougal Algebra 1
Factoring Polynomials continued
Factor each trinomial.
13. 45x
2 + 42x + 8
________________________________________
14. 28a2 + 11a − 30
________________________________________
15. −10x
2 + 19x + 15
________________________________________
Determine whether the trinomial is a perfect square. If so, factor it. If not, explain why.
16. 81n
2 + 90n + 100
________________________________________
________________________________________
17. 49x
2 − 182x + 169
________________________________________
________________________________________
Determine whether the binomial is a difference of two squares. If so, factor it. If not, explain why.
18. 121p2 − 40
________________________________________
________________________________________
19. 64x
6 − y
2
________________________________________
________________________________________
20. The area of a square in square feet is
represented by 625z
2 − 150z + 9. Find an
expression for the perimeter of the
square. Then find the perimeter when
z = 15 ft.
expression: ____________________________
perimeter when z = 15 ft: _______________
21. Tell whether 3x(2x
2 + 3x − 30) is
completely factored. If not, factor it.
________________________________________
________________________________________
Factor each polynomial completely.
22. 4x2 y + 72xy + 324
________________________________________
23. 36m
3 + 9m
2 − 4m − 1
________________________________________
SECTION
8
Name _______________________________________ Date __________________ Class __________________
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177 Holt McDougal Algebra 1
Quadratic Functions and Equations
1. Tell whether this function is quadratic.
Explain.
{(−7, 256), (−5, 16), (−3, 0), (−1, 16)}
________________________________________
________________________________________
2. Identify the vertex of this parabola. Then
give the minimum or maximum value of
the function.
vertex: _________________________________
________________________________________
3. Use a table of values to graph
y = 3x
2 − 8.
x −2 −1 0 1 2
y
4. Find the zeros of y = x
2 + 4x + 5 from its
graph below.
________________________________________
5. Find the axis of symmetry and vertex of
the graph of y = −2x
2 − 20x − 40.
axis of symmetry: ______________________
vertex: _________________________________
6. If you graph 2y + 8 = 6x
2 − 10x, what will
be the y-intercept?
________________________________________
7. The height of a ball in meters is modeled
by f(x) = −5x
2 + 36x, where x is the time
in seconds after it is hit. How long is the
ball in the air?
________________________________________
SECTION
9
Name _______________________________________ Date __________________ Class __________________
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178 Holt McDougal Algebra 1
Quadratic Functions and Equations continued
8. Use this graph of the quadratic function
y = −x
2 + 2x to solve the equation
−x
2 + 2x = 0.
________________________________________
9. Solve 26x + 15 = −8x2 by factoring.
________________________________________
10. A 6-foot tall soccer player bunts the ball
with his head. The ball’s height above
the ground is modeled by
h = −16t
2 − 10t + 6, where h is height in
feet and t is time in seconds. Find the
time it takes the ball to reach the ground.
________________________________________
11. Solve x
2 = −400 using square roots.
________________________________________
12. Solve (x − 5)2 = 36 using square roots.
________________________________________
13. Complete the square to form a perfect
square trinomial.
x2 +
3
5x + _________________
14. Solve 2x
2 + x + 8 = 0 by completing
the square.
________________________________________
15. Solve 3x + 1 = 5x
2 using the Quadratic
Formula.
________________________________________
16. Find the number of real solutions of the
equation −4x
2 + 6 = −7x using the
discriminant.
________________________________________
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9
Name _______________________________________ Date __________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
197 Holt McDougal Algebra 1
Radical and Rational Expressions
1. Simplify
468
100.
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2. A 15-foot ladder leans against a wall
with its base 5 feet from the wall. How
high up on the wall does the ladder
reach? Give your answer as a radical
expression in simplest form.
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3. Simplify
72x3y 4 . The variables
represent a nonnegative numbers.
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4. Add 28a + 98a + 3 2a.
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5. Subtract 500 − 20.
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6. Multiply 5x( 30x + 10) and write the
product in simplest form.
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7. Multiply (6 − 2)2 and write the
product in simplest form.
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8. Simplify the quotient
45
5 a.
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9. Find any excluded values of
c2 + 7c +10
c2 + 2c.
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Simplify, if possible.
10.
3x2 − x
6x2 + x −1
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11.
10 − 2k
k 2 − 25
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Name _______________________________________ Date __________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
198 Holt McDougal Algebra 1
Radical and Rational Expressions continued
Multiply. Simplify your answer.
12.
21m4n3
25n9p4g
30m3n6p15
28m6
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13.
2x2 − 2x − 12
x2 + 6x + 8g
x2 − 16
2x2 − x − 15
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14. Divide
3n2+19n + 6
n − 3 ÷ (n2 + 3n − 18).
Simplify your answer.
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15. Add
3a2 −15a −10
a2 + 4a −12 +
2a2 + 35a − 50
a2 + 4a −12.
Simplify your answer.
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16. Find the LCM of p2 − 36 and
p2 + 4p − 12.
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17. Subtract
x2 + x
x2 + 6x − 7 −
x + 3
3x + 21.
Simplify your answer.
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Divide.
18. (18y2 − 6y + 1) ÷ (−6y2)
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19.
6b2+10b − 4
b + 2
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20. (5n3 − 18n2 − 8) ÷ (n − 4)
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Solve. Check your answer.
21.
1
x =
x − 3
x2 − 9
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22.
t
t − 3 +
t
2 =
6t
2t − 6
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23. Pipe A fills a tank in 9 hours. Pipe B fills
the tank in 6 hours. How long would it
take both pipes to fill the tank?
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Name _______________________________________ Date __________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
217 Holt McDougal Algebra 1
Probability and Data Analysis
An experiment consists of rolling a number cube. Use these results for questions 1 and 2.
Outcome 1 2 3 4 5 6
Frequency 24 10 8 3 30 15
1. What is the experimental probability of NOT rolling a 6?
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2. If James rolls the number cube 250 times, predict the number of times it will land on an odd number.
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3. Find the theoretical probability of choosing a multiple of 5 from a standard deck of playing cards.
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4. The odds against picking a red marble from a bag are 4:3. What is the probability of picking a red marble?
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5. Two number cubes are rolled 3 times in a row. What is the probability of rolling a sum of 9 all three times?
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6. A kitchen drawer contains 8 forks, 8 spoons, and 6 knives. Jordan randomly picks two utensils without replacing the first. What is the probability that he gets two forks?
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7. The number of points scored by two football teams during the first half of the 2004 season are given below. Use the data to make a stem-and-leaf plot. 49ers: 19, 27, 0, 14, 31, 14, 13, 27 Raiders: 21, 13, 30, 17, 14, 3, 26, 14
The fuel economy in miles per gallon (mi/gal) of several vehicles are given below. Use this data for questions 8-10.
miles per gallon
28.5 18.0 19.6 21.1 22.0 24.0 16.9
27.2 15.2 18.0 21.5 29.0 18.0 28.0
8. Complete this frequency table.
mi/gal Frequency
15-17.9
18-20.9
21-23.9
24-26.9
27-29.9
Then use your frequency table to make a histogram.
9. Find the mean, median, and mode. (Round answers to the nearest tenth.)
mean: _________________
median: _________________
mode: _________________
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Name _______________________________________ Date __________________ Class __________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
218 Holt McDougal Algebra 1
Probability and Data Analysis continued
10. Use the data to make a box-and-whisker plot.
11. From 12 prepared songs, a band chooses 3 to perform on a TV show. One song will be played at the beginning of the show, one in the middle, and one at the end. Tell how many different set lists are possible. Then tell if the situation involves permutations or combinations.
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12. A carnival game costs $2. Players win a prize worth $6 if they spin a 6 or a prize worth $4 if they spin a 4 on the spinner shown. What is the expected profit or loss when the game is played once?
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13. When sketching a normal curve, what value represents one standard deviation to the right of the mean for the data set? 56, 54, 45, 52, and 48.
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14. The amount of juice in a container is normally distributed with a mean of 70 ounces and a standard deviation of 0.5 ounce. What is the probability that a randomly selected container has more than 70.5 ounces of juice?
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15. Marissa surveys four classmates about their favorite restaurant. Three classmates answer McBurger, and one answers Salad Stop. Explain why the following statement is misleading: “McBurger is the favorite restaurant of a majority of students.”
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